Great question, I am following with interest. I tried Chesskid for my group then switched to Lichess.. The Chesskid had better training videos and a nice step by step progression for children. However it lacked the most basic elements. Kids in my Zoom class could not challenge each other to 5 and 10 minute games. The tournament function was buggy and didn't work. Lichess is great for challenging friends to any time control and widely used by clubs for tournaments. Even if its training mater does not look great. Lichess is also free.
Neither allow for one kid to practise simple checkmates or K+P vs K end games against each other, which is a shame. I have heard that chessity allows that but ghat it's paying and I haven't tried it.

Am starting up a few elementary school (2nd-5th grade) chess clubs this Fall. Need to select a chess CLM system. Has anyone published their comparisons between the scholastic teaching tools and classroom (club) management offerings of Chessity, Chesskid, Chess4Life, Chessable, ChessMagnetSchool, Zoomchess, LiChess, LearningChess, etc? A side-by-side comparison? Anywhere?